

A098383


Define a function f on the positive integers by: if n is 1 or composite, stop; but if n = prime(k) then f(n) = k; a(n) = sum of terms in trajectory of n under repeated application of f.


1



1, 3, 6, 4, 11, 6, 11, 8, 9, 10, 22, 12, 19, 14, 15, 16, 28, 18, 27, 20, 21, 22, 32, 24, 25, 26, 27, 28, 39, 30, 53, 32, 33, 34, 35, 36, 49, 38, 39, 40, 60, 42, 57, 44, 45, 46, 62, 48, 49, 50, 51, 52, 69, 54, 55, 56, 57, 58, 87, 60, 79, 62, 63, 64, 65, 66, 94, 68, 69, 70, 91, 72
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OFFSET

1,2


COMMENTS

Sum of the terms in the prime index chain for n (cf. A049076).


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000
N. Fernandez, An order of primeness, F(p)
N. Fernandez, An order of primeness [cached copy, included with permission of the author]


EXAMPLE

a(2) = 3 because 2 is the first prime, therefore 2 + 1 = 3. a(3) = 6 because 3 is the second prime and two is the first prime, therefore 3 + 2 + 1 = 6. a(4) = 4 because 4 is composite. a(5) = 11 because five is the third prime, three is the second prime and two is the first prime, which gives us 5 + 3 + 2 + 1 = 11 and so on.


MAPLE

a:= n> n + `if`(isprime(n), a(numtheory[pi](n)), 0):
seq (a(n), n=1..80); # Alois P. Heinz, Jul 16 2012


MATHEMATICA

Table[s=n; p=n; While[PrimeQ[p], p=PrimePi[p]; s=s+p]; s, {n, 1000}] (T. D. Noe)


CROSSREFS

Cf. A007097, A057450, A057451, A049076.
Sequence in context: A122634 A169846 A169854 * A328637 A162523 A292681
Adjacent sequences: A098380 A098381 A098382 * A098384 A098385 A098386


KEYWORD

easy,nonn


AUTHOR

Andrew S. Plewe, Oct 26 2004


EXTENSIONS

More terms from Ray Chandler, Nov 04 2004


STATUS

approved



